14740 - Spiral Traversal   

Description

This problem is revised from example 6.27 of the textbook.

You are given an n x n matrix, where n is an odd integer.
Starting from the center of the matrix, traverse all elements in a counterclockwise spiral path.

The traversal must follow these rules:

  1. Direction order:
    Right → Up → Left → Down→ (repeat).

  2. Step lengths:

    • The number of steps in each direction follows the sequence 1,1,2,2,3,3,…

    • Each step length is repeated twice (for two consecutive directions).

    • The only exception is the last step length (n−1), which must be repeated three times to complete the outer boundary.

  3. Traversal stops when all n2 elements have been visited exactly once.

Input

  • The first line contains an odd integer n (1≤n≤99).

  • The next n lines each contain nnn integers, representing the matrix elements in row-major order.

Output

Print the elements of the matrix in the order they are visited by the spiral traversal, one element per line.

Sample Input  Download

Sample Output  Download




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